How can I extrude a dome from a circular face?
Yes, try extruding and scaling it multiple times:



To help make the extrusions more even, you might try using the To Sphere operator (&#9095; Alt&#8679; ShiftS). You can define where the center of the "sphere" To Sphere uses by using the 3D cursor as the pivot (.).

If you want to be more precise, try adding a sphere and deleting half, then using Bridge edge loops (W, E)



Note that the number of vertices on the perimeter of the sphere should match the number of vertices around the initial circle.